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Mathematics
Mathematics
Problem
Solve
sin
2
θ
=
cos
θ
\sin 2\theta = \cos\theta
sin
2
θ
=
cos
θ
for
θ
\theta
θ
in
(
0
,
2
π
)
(0,2\pi)
(
0
,
2
π
)
. a)
θ
=
π
6
,
π
2
,
5
π
6
,
3
π
2
\theta = \dfrac{\pi}{6},\;\dfrac{\pi}{2},\;\dfrac{5\pi}{6},\;\dfrac{3\pi}{2}
θ
=
6
π
,
2
π
,
6
5
π
,
2
3
π
b)
θ
=
π
3
,
π
2
,
π
,
3
π
2
\theta = \dfrac{\pi}{3},\;\dfrac{\pi}{2},\;\pi,\;\dfrac{3\pi}{2}
θ
=
3
π
,
2
π
,
π
,
2
3
π
c)
θ
=
π
6
,
π
2
,
5
π
6
\theta = \dfrac{\pi}{6},\;\dfrac{\pi}{2},\;\dfrac{5\pi}{6}
θ
=
6
π
,
2
π
,
6
5
π
d)
θ
=
π
6
,
π
2
,
3
π
2
\theta = \dfrac{\pi}{6},\;\dfrac{\pi}{2},\;\dfrac{3\pi}{2}
θ
=
6
π
,
2
π
,
2
3
π
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